Our method seeks a pairwise distance measure between 3D keypoint sets. As different images generally contain different numbers of elements, a natural choice for pairwise distance between variable sized sets are measures based on set intersection or overlap, e.g. the Jaccard distance metric [1]} first proposed in [2]} or the Tanimoto distance [3]}, [4]}. In medical image analysis, the Jaccard distance is typically used to assess pixel-level segmentation accuracy [5]}, and has proven highly effective for assessing pairwise neuroimage similarity from 3D SIFT keypoint data [6]}, [7]}, where hard set equivalence is determined by NN keypoint descriptor correspondences.
Set theory is predicated on binary equivalence between set elements, which is difficult to justify in the case of keypoints extracted from image data. Soft set theory was been developed to account for non-binary equivalence [8]}, [9]}, [10]}, where set operations including intersection and union are defined in terms of non-binary equivalence ranging from [0,1]. Jaccard-like distance was used for retrieving near-duplicate 2D photos [11]}, where the ratio of soft intersection and union operators was used to account for document frequency. Our work here extends the Jaccard distance proposed in [12]} to include keypoint geometry in 3D Euclidean metric space coordinates, and compares to the HSE Jaccard measure used in [6]}, [7]}, showing a significant improvement in predicting family relationships.
